Related papers: Fast Matrix Multiplication meets the Submodular Wi…
Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
Uniform sampling and approximate counting are fundamental primitives for modern database applications, ranging from query optimization to approximate query processing. While recent breakthroughs have established optimal sampling and…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a…
The co-design of neural network architectures, quantization precisions, and hardware accelerators offers a promising approach to achieving an optimal balance between performance and efficiency, particularly for model deployment on…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Finding the common structural features of two molecules is a fundamental task in cheminformatics. Most drugs are small molecules, which can naturally be interpreted as graphs. Hence, the task is formalized as maximum common subgraph…
Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an…
We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the "s-rank exponent of matrix…
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…
Reinforcement learning has witnessed significant advancements, particularly with the emergence of model-based approaches. Among these, $Q$-learning has proven to be a powerful algorithm in model-free settings. However, the extension of…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…
We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…